## Elements of Geometry |

### From inside the book

Results 1-5 of 11

Page iii

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**spherical**isoperimetrical**polygons**, and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . Also an improved demonstration of the theorem for the solidity retation Presented to. Page vii

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**sphere**and**spherical**triangles . This treatise does not ordina- rily make a part of the elements of geometry ; still we have thought it proper to consider so much of it as may form an intro- duction to**spherical**trigonometry . The ... Page 174

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**spherical**pyramids are to each other as the**polygons**which constitute their bases . 2. The solid angles at the**vertex**of these same pyramids are likewise proportional to the bases ; therefore , in order to com- pare any two solid angles ... Page 189

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**spherical**triangles , the ratio of which to the entire surface of the**sphere**has already been determined . In the ...**polygons**follows immediately from that of triangles , and it is moreover entirely determined by the proposition of art ... Page 199

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**spherical**segment have only one base P , its solidity will be PH + ¦ л H3 . 14 Appendix to the Third Section of the Second Part . OF**SPHERICAL**ISOPERIMETRICAL**POLYGONS**. THEOREM . 556. Let S be the number of solid angles in a polyedron ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence